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Extending continuous functions defined on subsets of products
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Extending continuous functions defined on subsets of products
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Description
Identifier
Thesis
2195
Author
Rivers, Douglas Michael, 1984
Title
Extending
continuous
functions
defined
on
subsets
of
products
Publisher
Central Connecticut State University;
Date of Publication
2011
Resource Type
Master's Thesis
Abstract
Let
X
and
Z
be
topological
spaces
and
Y
be a
subspace
of
X
. A
con
tinuous
function
f
:
Y
!
Z
is
extendable
to
X
if there
exists
a
continuous
function
f
:
X
!
Z
such
that
f(x)
=
f(x)
for
all
x
2
Y
. If
every
continuous
function
f
:
Y
!
Z
is
extendable
to
X
then
Y
is
called
C(Z)embedded
in
X
.
According
to
R
.
Engelking
,
\theorems
that
give
su
cient
conditions
for
extendability
of
continuous
mappings
of
continuous
realvalued
functions
are
among
the
most
important
ones
in
topology
, and
usually
are
rather
di
cult.
" In this
thesis
we
analyze
three
such
theorems
by
Milton
Ulmer
that
ap
peared
in his
paper
Cembedded
spaces
,
Paci
c
J
.
Math
,
46
(1973)
,
591{
602
, and
some
results
generalizing
two
of the
Ulmer's
theorems
that
appeared
recently
in
two
papers
by
W
.
W
.
Comfort
and
Ivan
S
.
Gotchev
:
Continuous
Mappings
on
Subspaces
of
Products
with the
box
Topology
,
Topology
Appl
.
156
(2009)
,
No
.
16
,
2600{2608
and
Continuous
Extensions
of
Functions
De
ned
on
Subsets
of
Products
,
accepted
for
publication
in
Topology
Appl
.
After
that
we
formulate
and
prove
a
theorem
that
signi
cantly
generalizes
two
of the
Ulmer's
theorems
and a
theorem
by
W
.
W
.
Comfort
and
Ivan
S
.
Gotchev
. This
contribution
to the
topic
is
a
joint
work
with
W
.
W
.
Comfort
and
Ivan
S
.
Gotchev
.
Subject
Topology
Topological spaces
Department
Department of Mathematical Sciences
Advisor
Gotchev, Ivan S.
Type
Text;
Digital Format
application/pdf
Language
eng
OCLC number
804653037
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